Two Methods for Reducing the Error-Floor of LDPC Codes

We investigate two techniques for reducing the error-floor of low-density parity-check codes under iterative decoding. Both techniques are developed based on comprehensive analytical and simulation studies of combinatorial properties of trapping sets in codes on graphs. The first technique represents an algorithmic modification of beliefpropagation based on data fusion principles and specialized message averaging methods. The second technique relies on identifying redundant parity-check matrices of codes that do not contain small trapping sets. In the latter context we introduce the notion of the trapping redundancy of a code and show how decoding with redundant parity-check matrices can lead to reductions of error rates exceeding an order of magnitude. Our findings are described on the well known [2640,1320] Margulis code.